Apparatus, method, mobile station and computer program product for noise estimation, modeling and filtering of a digital image

ABSTRACT

An apparatus, method, mobile station and computer program product are provided for filtering noise from a digital signal. In particular, a signal-dependent noise model is used that provides the pointwise (or pixelwise) standard deviation of the temporal noise of raw data outputted from a digital imaging sensor as a function of the image intensity. In addition, unlike conventional noise models, the standard deviation of the noise (σ) is a parameterized function, where the parameters are key characteristics of the digital imaging sensor. These parameters may include, for example, the pedestal level (p), the quantum efficiency (q), and the analogue gain (α) associated with the digital imaging sensor.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation-in-part of U.S. patent applicationSer. No. 11/426,128, filed Jun. 23, 2006, now abandoned which is herebyincorporated herein in its entirety by reference.

FIELD

Exemplary embodiments of the present invention relate, generally, todigital image processing and, in particular, to digital imaging sensornoise modeling.

BACKGROUND

Progress in digital imaging hardware design has introduced digitalimaging sensors having a dramatically increased number of pixels, orpixel density (i.e., having an increase in the sensor's resolution).While beneficial for many reasons, this results in the size of eachpixel becoming smaller and smaller and, therefore, the sensor outputsignal's susceptibility to noise becoming greater and greater.

In order to attenuate the noise in the most efficient way, it isimportant that proper modeling of the noise is considered during digitalimage processing. However, modeling of noise can be difficult since,when utilizing, for example, a digital camera, the images are likelytaken under different illumination conditions and different ambienttemperatures. In addition, the digital imaging sensor itself may applydifferent exposure and/or analogue gain settings, or the like. In otherwords, the noise that results from digital sensing can vary from imageto image. Because of inherent photoelectric conversion, the noise ispredominantly signal-dependent. A single non-adaptive image processingfilter may, therefore, not be useful for all pictures taken under thesevarying conditions.

Despite this, current filtering algorithms typically assume independentstationary noise models (i.e., signal-independent), and even where asignal-dependent model is assumed, the correct parameters for the noiseare often not specified.

Recently, several complete models have been proposed, which explicitlytake into account most of the elements that can potentially contributeto the sensor's noise (e.g., dark signal level, Fixed-Pattern Noise,Shot-noise Photonic (Poissonian noise), dark current noise, dark currentnon-uniformity, photo-response non-uniformity, amplifier noise, circuitnoise, thermal noise, pixel cross-talk, correlated double sampling,quantization noise, chromatic conversions, etc.). (See R. Costantini andS. Süsstrunk, “Virtual Sensor Design”, Proc. IS&T/SPIE ElectronicImaging 2004: Sensors and Camera Systems for Scientific, Industrial, andDigital Photography Applications V, 2004, Vol. 5301, pp. 408-419; H.Wach and E. R. Dowski, Jr., “Noise modeling for design and simulation ofcomputational imaging systems”, Proceedings of SPIE—Volume 5438 VisualInformation Processing XIII, Zia-ur Rahman, Robert A. Schowengerdt,Stephen E. Reichenbach, Editors, July 2004, pp. 159-170 (referred tohereinafter as “Wach”); and A. J. Blanksby and M. J. Loinaz,“Performance analysis of a color CMOS photogate sensor,” IEEE Trans.Electron Devices, vol. 47, no. 1, pp. 55-64, January 2000). While theseproposed models provide an accurate modeling of each individualcontributor to the noise, the large number of parameters contemplated bythese complex models makes them eventually unpractical for modeling theoverall sensor's noise. Some of the model parameters may implicitlydepend on other parameters (posing serious limitations to theirestimation, as it is often not possible to estimate many parameterssimultaneously with sufficient precision), and some may belong to theinner-workings of the sensor itself and, therefore, may not be known byother than the sensor's manufacturer. In practice, it is thus arguablyimpossible to achieve any faithful approximation of the overall sensor'snoise by means of these much-articulated models. Further, these modelstreat color channels separately, obtaining different noise parametersfor different channels.

In addition, most research literature available on sensor noise analysiswas developed within the electronic engineering community and typicallycomes to conclusions and models which are useful and significant mainlyfor the purpose of electronic hardware design and integration (e.g.,dimensioning of the device, interfacing, shielding, etc.). (See H. Tian,B. Fowler, and A. El Gamal, “Analysis of Temporal Noise in CMOSPhotodiode Active Pixel Sensor,” IEEE Journal of Solid-State Circuits,vol. 36, no. 1, pp. 92-101, January 2001). The literature providesresults that are of a global nature (i.e., provides noise figures whichare valid and accurate for the whole sensor). However, such global noiseestimates are rough when applied to an individual pixel of the sensor.These models, therefore, are inadequate for high-quality imageprocessing applications, such as de-noising or de-blurring, since thesetechniques require accurate pointwise (i.e., pixelwise) knowledge of thenoise, in order to properly restore the image details.

A need, therefore, exists for a more accurate and usable noise modelthat can be placed in the imaging chain for use in de-noising,de-blurring, and other digital image processing tasks (e.g., colorinterpolation, sharpening, etc.).

BRIEF SUMMARY

In general, exemplary embodiments of the present invention provide animprovement over the known prior art by, among other things, providing asignal-dependent noise model that provides the pointwise (or pixelwise)standard deviation of the temporal noise of raw data outputted from adigital imaging sensor as a function of the image intensity. In oneexemplary embodiment, the standard deviation of the noise (σ) is aparameterized function, where the parameters are key characteristics ofthe digital imaging sensor. These parameters may include, for example,the pedestal level (p), the quantum efficiency (q), and the analoguegain (α) associated with the digital imaging sensor.

In accordance with one aspect, an apparatus is provided. In oneexemplary embodiment, the apparatus comprises: (1) an input forreceiving data representative of an intensity of an image at a pixelposition; (2) a processing element for filtering the data to removenoise, wherein the processing element filters the data based on at leastone parameter associated with one or more characteristics of a sensorthrough which the image was captured; and (3) an output for providingthe filtered data.

In one exemplary embodiment the processing element filters the databased on a signal-dependent noise model defined based on the at leastone parameter associated with one or more characteristics of the sensor.In another exemplary embodiment, the processing element determines astandard deviation of the noise as a function of the intensity of theimage at the pixel position. This may include, for example, determiningthe standard deviation based on at least one of a quantum efficiency(q), a pedestal level (p), or an analogue gain (α) associated with thesensor. In particular, in one exemplary embodiment, the standarddeviation is determined in accordance with

${{\sigma^{\lbrack\alpha\rbrack}(y)} = {{\alpha\; q\sqrt{\frac{y - p}{\alpha}}} = {q\sqrt{\alpha\left( {y - p} \right)}}}},$wherein y represents the intensity of the image at the pixel position.

In accordance with another aspect, a method is provided of filteringnoise from a digital image. In one exemplary embodiment, the methodincludes: (1) receiving data representative of an intensity of an imageat a pixel position; (2) filtering the data to remove noise, wherein theprocessing element filters the data based on at least one parameterassociated with one or more characteristics of a sensor through whichthe image was captured; and (3) providing the filtered data.

According to one aspect, a mobile station is provided for filteringnoise from a digital image. In one exemplary embodiment the mobilestation includes a processor and a memory in communication with theprocessor that stores an application executable by the processor,wherein the application is configured, upon execution, to: (1) receivedata representative of an intensity of an image at a pixel position; (2)filter the data to remove noise, wherein the processing element filtersthe data based on at least one parameter associated with one or morecharacteristics of a sensor through which the image was captured; and(3) provide the filtered data.

According to another aspect an apparatus is provided that, in oneembodiment, includes: (1) means for receiving data representative of anintensity of an image at a pixel position; (2) means for filtering thedata to remove noise, wherein the processing element filters the databased on at least one parameter associated with one or morecharacteristics of a sensor through which the image was captured; and(3) means for providing the filtered data.

In accordance with yet another aspect, a computer program product isprovided for filtering noise from a digital image. The computer programproduct contains at least one computer-readable storage medium havingcomputer-readable program code portions stored therein. Thecomputer-readable program code portions of one exemplary embodimentinclude: (1) a first executable portion for receiving datarepresentative of an intensity of an image at a pixel position; (2) asecond executable portion for filtering the data to remove noise,wherein the processing element filters the data based on at least oneparameter associated with one or more characteristics of a sensorthrough which the image was captured; and (3) a third executable portionfor providing the filtered data.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING(S)

Having thus described exemplary embodiments of the invention in generalterms, reference will now be made to the accompanying drawings, whichare not necessarily drawn to scale, and wherein:

FIG. 1 represents a family of standard deviation curves that can bederived for different analogue gain values in accordance with exemplaryembodiments of the present invention;

FIGS. 2A and 2B represent the measured standard deviation curves, andcorresponding fitted model, based on raw data related to two differentCMOS sensors U and V, respectively, in accordance with exemplaryembodiments of the present invention;

FIG. 2C represents the theoretical standard deviations curves associatedwith CMOS sensors U and V, respectively, in accordance with exemplaryembodiments of the present invention;

FIG. 2D represents the standard deviation curve, and corresponded fittedmodel, based on raw data related to CMOS sensor V for a differentexposure time, in accordance with exemplary embodiments of the presentinvention;

FIGS. 3A-3F represent the measured values for standard deviation as afunction of the intensity of the signal, and the corresponding fittedfunction, for different gain parameters, in accordance with exemplaryembodiments of the present invention;

FIG. 4 is a block diagram illustrating the offline calibration andonline image capture process of exemplary embodiments of the presentinvention;

FIGS. 5A and 5B illustrate the improved signal quality that can beachieved using the noise model of exemplary embodiments of the presentinvention; and

FIG. 6 is a schematic block diagram of a mobile station capable ofoperating in accordance with an exemplary embodiment of the presentinvention;

DETAILED DESCRIPTION

Exemplary embodiments of the present invention now will be describedmore fully hereinafter with reference to the accompanying drawings, inwhich some, but not all embodiments of the inventions are shown. Indeed,exemplary embodiments of the invention may be embodied in many differentforms and should not be construed as limited to the embodiments setforth herein; rather, these embodiments are provided so that thisdisclosure will satisfy applicable legal requirements. Like numbersrefer to like elements throughout.

Overview:

In general, exemplary embodiments of the present invention provide asignal-dependent noise model for raw data of a digital imaging sensor(e.g., a Complementary Metal-Oxide Semiconductor (CMOS) orCharge-Coupled Device (CCD) sensor), which can be plugged into acorresponding generic image processing filter of an imaging device(e.g., a digital camera, cameraphone, webcam, etc.) in order to optimizethe final imaging quality. Exemplary embodiments further provide acalibration methodology that can be used to estimate the parameters ofthe noise model.

In particular, the noise model of exemplary embodiments provides thepointwise (or pixelwise) standard deviation of the temporal noise of theraw data as a function of the image intensity. In other words, everypixel of the image is considered with an individual estimate of itsvariance.

As a consequence of this modeling, the standard deviation versusintensity curve does not depend on the color-channel or exposure timeassociated with the signal at an individual pixel position. This is aremarkable difference from conventional noise models for imagingsensors, in which the level of noise depends on the color-channel andthe exposure time, resulting in conventional noise models beingdifficult to use in practical implementation, since they require thatthe de-noising algorithm be aware of both the color-channel and exposuresettings.

The signal-dependent noise model of exemplary embodiments of the presentinvention can be described by three parameters, which aresensor-dependent and can be identified easily at the manufacturingstage. These parameters are further capable of being adjusted later(i.e., to calibrate or recalibrate the sensor).

Implementation of the noise model of exemplary embodiments within theimaging chain allows the performance of accurate digital filtering ofthe raw data, and, in particular, de-noising and de-blurring by usingalgorithms suitable for signal-dependent noise.

Theoretical Modeling of Noise:

The following illustrates how the noise model of exemplary embodimentsof the present invention can be derived.

First observe the generic noise model of the form:z(x)=y(x)+σ(y(x))ξ(x)  Equation 1

where x is the pixel position, y is the intensity of the original image,ξ is a random noise element with a standard deviation equal to 1, and σ,which is a function of the intensity (i.e., of y), modulates thestandard deviation of the overall noise component. The random noise ξ(x)is zero-mean, hence E{z(x)}=y(x). Therefore, std[z(x)]=σ(E{z(x)}), wherestd stands for the standard deviation. No other restriction is placed onthe distribution of ξ(x), and different pixels may have differentdistributions.

Let z(x) be the Poisson process. Conceptually, this stochastic modelcorresponds to the counting process of the photons that fall on thesmall photo-sensitive pixel area. The standard “ideal” model for thePoissonian observations implies that the variance is equal to the mean:var{z(x)}=E{z(x)}  Equation 2

Thus, Equation 1 takes the form:z(x)=y(x)+√{square root over (y(x))}ξ(x)  Equation 3

The proposed approximate Poissonian model is modified essentially, withrespect to Equation 3, by introducing three parameters, which relate tospecific aspects of the digital sensor's hardware. These parameters,which are discussed in more detail below, include: quantum efficiency,pedestal level and analogue gain. The result of introducing theseparameters into the noise model is a link between the expectation andthe variance that is different from that of the ideal model (i.e.,Equation 3).

Scale Parameter: Incorporating the Quantum Efficiency (q):

In practice, acquisition systems do not have an ideal response to thecollected photons, and, typically, a large number of photons are used toproduce a response of the sensor. This means that, with respect to theideal case, the intensity of the photon flow is reduced by a scalarfactor. The impact of this factor on the observation model is expressedby a coefficient q appearing as a multiplier in front of the noise term:z(x)=y(x)+q√{square root over (y(x))}ξ(x)σ(y)=q√{square root over (y)}  Equation 4

The value of q affects the intensity-dependent signal-to-noise ratio(SNR) of the imaging sensor,

$\begin{matrix}{{{SNR}(y)} = {\frac{y}{\sigma(y)} = \frac{\sqrt{y}}{q}}} & {{Equation}\mspace{14mu} 5}\end{matrix}$

The coefficient q is related to the so-called quantum efficiency of thesensor's pixel, i.e., the charge-photons ratio, and larger values of qcorrespond to a lower (or worse) signal-to-noise ratio.

Pedestal Parameter (p):

In digital imaging sensors, the collected charge always starts from somesmall base, or “pedestal” level. This constitutes an offset-from-zero ofthe recorded data:z(x)=z ₀(x)+p  Equation 6

Here z is the raw data, z_(o) is the collected charge and p is thepedestal level. The pedestal level is typically subtracted from the rawdata after processing, in order to improve the image contrast.

The pedestal does not affect the standard deviation, but only relates toa shift in the intensities. It then follows that Equation 4 istransformed into:z(x)=y ₀(x)+p+q√{square root over (y ₀(x))}ξ(x)  Equation 7

where y₀=E{z₀} is the signal of interest, and y(x)=y₀(x)+p=E{z(x)} isthe expectation of the raw data. In terms of the raw data and itsexpectation only, Equation 7 can be rewritten as:z(x)=y(x)+q√{square root over (y(x)−p)}ξ(x)  (x) Equation 8

and, thus, the standard deviation of z(x) is:σ(y)=q√{square root over (y−p)}  Equation 9

Note that, according to the Poissonian modeling, aspects, such as theexposure-time or the wavelength of the light, do not appear in the aboveequations. However, they are implicitly, or more precisely,automatically, taken into account. For example, increasing the exposuretime causes the number of collected photons to increase proportionallyresulting in an increased in the intensity of the recorded data.Consequently, the SNR also increases. In a similar fashion, differentcolor filters allow different proportions of the incoming photons topass towards the sensor, depending upon the wavelength of the light.This causes a decrease in the number of collected photons, andconsequently a lowering of the SNR, when the intensity of the consideredcolor band is lower (e.g., blue channel typically has a lower SNR).

Analogue Gain Parameter (α):

The above model applies to any raw data taken without analogue gain(i.e., 0 dB). Analogue gain is then modeled as an amplification of thecollected charge. In other words, the collected charge (i.e., roughlyspeaking, the number of collected photons) is multiplied by a gainparameter α>1 prior to being read out of the sensor. This requires thata clear distinction be made between what is the collected charge andwhat is the raw data, which is read from the sensor.

Where z₀ denotes the collected charge, z^([α]) denotes the raw datacorresponding to a gain parameter α. For no gain, α=1 andz ^([1])(x)=z ₀(x)+p  Equation 10

while, for a generic α:z ^([α])(x)=αz ₀(x)+p=α(z ^([1])(x)−p)+p  Equation 11

In the previous section, the model Equation 9 was derived, which givesthe standard deviation std{z^([1])} of the raw data z^([1]) as afunction α^([1]) of its expectation E{z^([1])},std{z ^([1])(x)}=σ^([1])(E{z ^([1])(x)})=q√{square root over (E{z^([1])(x)}−p)}  Equation 12

Now, a similar function σ^([α]) should be found, such thatstd{z ^([α])(x)}=σ^([α])(E{z ^([α])(x)})  Equation 13

By considering the impact of the addition of a scalar, or multiplicationby a scalar, on the standard deviation of the random variable, one canobtain:std{z ^([α])(x)}=std{α(z ^([1])(x)−p)+p}=α·std{z^([1])(x)}=α·σ^([1])(E{z ^([1])(x)})  Equation 14

Since

$\begin{matrix}{z^{\lbrack 1\rbrack} = {\frac{z^{\lbrack\alpha\rbrack} - p}{\alpha} + p}} & {{Equation}\mspace{14mu} 15}\end{matrix}$

one arrives to the general form of σ^([α]) with respect to σ^([1]):

$\begin{matrix}{{{std}\left\{ {z^{\lbrack\alpha\rbrack}(x)} \right\}} = {{\alpha \cdot {\sigma^{\lbrack 1\rbrack}\left( {\frac{{E\left\{ {z^{\lbrack\alpha\rbrack}(x)} \right\}} - p}{\alpha} + p} \right)}} = {\sigma^{\lbrack\alpha\rbrack}\left( {E\left\{ z^{\lbrack\alpha\rbrack} \right\}} \right)}}} & {{Equation}\mspace{14mu} 16}\end{matrix}$Final Result:

By recalling Equation 9, one can formulate the final result:

$\begin{matrix}{{\sigma^{\lbrack\alpha\rbrack}(y)} = {{\alpha\; q\sqrt{\frac{y - p}{\alpha}}} = {q\sqrt{\alpha\left( {y - p} \right)}}}} & {{Equation}\mspace{14mu} 17}\end{matrix}$

which provides the standard deviation std{z[α]} of the raw data z[α] asa function of its expectation E{z[α]}. The parameter α is defined by theused gain. By varying the parameter α, Equation 17 yields the family ofcurves illustrated in FIG. 1. In particular, FIG. 1 represents thefamily σ^([α])(y)=q√{square root over (α(y−p))} for certain choices ofα≧1, where p and q are fixed values corresponding to the noise model ofa particular CMOS sensor from a Nokia cameraphone. Observe from FIG. 1that increasing a results in a higher curve representing a decrease ofthe SNR understood as

$\frac{y}{\sigma^{\lbrack\alpha\rbrack}(y)}.$Calibration Methodology for Estimation of Model Parameters:

The following illustrates how the parameters p and q (i.e., pedestallevel and quantum efficiency), which depend on the particular digitalsensor in use, can be determined and further how the noise model derivedabove can be validated.

The following assumes that a sufficient number N of shots of a fixedtarget has been taken under constant-in-time illumination. There are noparticular requirements of the target (even though in practice it wouldbe beneficial if the target exhibited portions of differentbrightness/darkness, so as to cover a wide range of intensities), thusenabling a generic fixed target image to be used. Observe that thisconstitutes a fundamental difference from previously publishedprocedures (See e.g., ISO 15739, “Photography—Electronic still-pictureimaging—Noise measurements,” (2003); Wach; and Hytti, H.,“Characterization of digital image noise properties based on RAW data,”Proceedings of SPIE—Vol. 6059, Image Quality and System Performance III,Luke C. Cui, Yoichi Miyake, Editors, 60590A Jan. 15, 2006), which assumethat a specific pattern or a uniform white plate is used as a target.Previous procedures exploit explicitly such particular nature of thetarget. However, several practical aspects make such a strategyidealistic. For example, when a uniform white plate is used as thetarget, the recorded image is never truly uniform because of theunavoidable non-uniformity of illumination and because of the vignettingeffect caused by the lens system of the camera in which the sensor ismounted. Consequently, the noise estimation implemented by previousprocedures is impaired by inherently biased measurements. Variousstratagems and compensations (e.g., “trend subtraction”) are typicallyintroduced to counteract these unwanted systematic errors. Nevertheless,an idealistic and unrealizable measurement scenario inevitably hampersthe accuracy and trustworthiness of the noise model parameters that canbe obtained from previously published procedures.

Averaging:

First, all of the shots N are averaged in order to obtain anapproximation of the noise-free y(x)

$\begin{matrix}{{\overset{\_}{z}(x)} = {{\frac{1}{N}{\sum\limits_{n = 1}^{N}\;{z_{n}(x)}}} = {{y(x)} + {\frac{1}{\sqrt{N}}{\sigma\left( {y(x)} \right)}\overset{\sim}{\xi}{(x).}}}}} & {{Equation}\mspace{14mu} 18}\end{matrix}$

Here, {tilde over (ξ)}(x) is again some zero-mean noise with a unitaryvariance. In experiments, up to N=50 shots can be taken, automaticallyand without touching the imaging device. It means that the pointwisestandard deviation in the average observation z is about 14% of the onefrom the individual shots z_(n).

Segmentation:

The average image z is then segmented into a number of non-overlappinguniform intensity regions {S}, or segments. Ideally, within theseregions, the intensity level of z(x) should be constant:S(y)={x: z (x)=y}.  Equation 19

However, this may lead to uncertain results, since there may be too few(or perhaps no) samples (i.e., pixels) that satisfy the equation z(x)=y.Pragmatically, it is convenient to consider a larger set of the formS _(Δ)(y)={x: z (x)ε[y−Δ/2,y+Δ/2)},  Equation 20

where Δ>0 is small.

Measurement of the Intensity-Dependent Standard Deviation:

The standard deviation is then computed independently for each shot asthe empirical estimate

$\begin{matrix}{{{{std}_{n}(y)} = \sqrt{\frac{\sum\limits_{m = 1}^{M}\;\left( {{z_{n}\left( x_{m} \right)} - {{\overset{\sim}{z}}_{n}(y)}} \right)^{2}}{M - 1}}},} & {{Equation}\mspace{14mu} 21}\end{matrix}$

where x_(m), m=1, . . . M are the coordinates of the pixels thatconstitute the segment S_(Δ)(y), and {tilde over (z)}_(n)(y) is the meanvalue of z_(n) over S_(Δ)(y),

$\begin{matrix}{{{\overset{\sim}{z}}_{n}(y)} = {\frac{1}{M}{\sum\limits_{m = 1}^{M}\;{{z_{n}\left( x_{m} \right)}.}}}} & {{Equation}\mspace{14mu} 22}\end{matrix}$

The final estimate of the standard deviation as a function of y is givenby the average over all N shots

$\begin{matrix}{{\overset{̑}{\sigma}(y)} = {\frac{1}{N}{\sum\limits_{n = 1}^{N}\;{{{std}_{n}(y)}.}}}} & {{Equation}\mspace{14mu} 23}\end{matrix}$Model Fitting and Validation:

Using the methodology described above, the standard deviation versusintensity curves have been measured from the sensor's raw data of twoexemplary Nokia cameraphones. The average value of the standarddeviation is obtained for each of four color channels. In other words,four curves {circumflex over (σ)}_(R)(y), {circumflex over (σ)}_(G) ₁(y), {circumflex over (σ)}_(G) ₂ (y) and {circumflex over (σ)}_(B)(y)have been computed independently, wherein R, G₁, G₂ and B refer to thefour channels of the Bayer-type pattern of the sensor.

It has been found that for α=1 (i.e., a gain of 0 dB), the standarddeviation function α^([1]) has the form:σ^([1])(y)=q√{square root over (y−p)}  Equation 24

With the following parameters:p_(u)=0.0060, q_(u)=0.050p_(v)=0.0092, q_(v)=0.021

where indices p_(u) and q_(u) refer to the parameters p and q associatedwith a first cameraphone sensor U, and p_(v) and q_(v) refer to theparameters p and q associated with a second cameraphone sensor V havingan increased pixel density relative to cameraphone sensor U, a nearlyperfect fit of the derived model to the measured data is enabled. Thiscan be seen from the plots illustrated in FIGS. 2A-2D.

In particular, FIGS. 2A and 2B illustrate the standard deviation curves,and corresponding fitted model, for the raw data of CMOS sensors U and Vfrom two cameraphones, respectively. Each of these figures includes rawdata from four separate color channels (R, G₁, G₂, and B), which arerepresented by different shades of gray. As can be seen, the noise modelof exemplary embodiments fits equally well with the data of all colorchannels (i.e., the standard deviation versus intensity curve does notdepend on the color-channel).

FIG. 2C provides a direct comparison between the standard deviationcurves of the two cameraphones, with the dashed line representing thestandard deviation curve of U, and the solid line representing thestandard deviation curve of V. As shown, cameraphone sensor V, which, asnoted above, has an increased pixel density, presents a lower SNR.Finally, FIG. 2D provides the noise model of exemplary embodimentsfitted on a standard deviation curve for cameraphone sensor V measuredfor a different exposure time; thus illustrating that the model furtherdoes not depend on exposure time.

As shown in FIGS. 3A-3F, which provide the measured values for thestandard deviation as a function of the intensity y, and thecorresponding fitted function, the validity of the above-derived noisemodel can be verified for a number of values of the gain parameter. Inparticular, FIGS. 3A-3F, respectively, illustrate that the noise modelfits the raw data for gains of 0, 4, 6, 8, 10 and 15 dB. Thecorresponding values of the parameter σ of the model of Equation 17 are,respectively, 1, 1.5, 2.1, 2.7, 2.9 and 6. The derived model fits quiteaccurately to the data. In fact, with the exception of the last value ofthe gain, which is rather large, the fit is nearly perfect. In addition,as with FIGS. 2A-2D, the plots of FIGS. 3A-3F include raw data from fourseparate color channels (shown by data of varying shades of gray),further illustrating that the standard deviation versus intensity curvedoes not depend on the color channel.

Use of the Signal-Dependent Noise Model in Digital Image Processing:

Referring now to FIG. 4, a block diagram of the above-describedcalibration process, as well as of the online image capture process, isprovided. As shown, and as discussed above, the values of p and q for aparticular digital imaging sensor are first determined by: (1) averagingN shots or images of a generic fixed target image; (2) segmenting theaverage image into a number of uniform intensity regions; (3) computingthe standard deviation versus intensity curve (i.e., the standarddeviation as a function of the intensity) for each shot to obtain anempirical “per shot” estimate, and computing a final estimate of thestandard deviation versus intensity curve by averaging the standarddeviations over all N shots; (4) fitting the derived model, which isbased on p and q, to the computed standard deviation versus intensitycurve in order to (5) determine a specific p and q associated with thedigital imaging sensor. Using the determined values of p and q, asensor-specific signal-dependent noise model (i.e., a calibrated model)can be generated.

According to exemplary embodiments, the calibration process describedabove is valid and accurate regardless of the particular noise model(e.g., Poissonian), and can, therefore, be used to estimate standarddeviation versus intensity curves of radically different noise models.In one exemplary embodiment, one could avoid model fitting altogether bystoring the estimated standard deviation versus intensity curves, forexample, in a look-up table (LUT), and using the curves directly forde-noising and de-blurring.

In one exemplary embodiment, the calibrated model may be stored in thedigital device (e.g., the digital camera, cameraphone, webcam, etc.) foruse in filtering the noise from an image captured by the digital imagingsensor.

In particular, as shown in FIG. 4, a processing element, such as anadaptive filter, may receive raw data associated with an image from thedigital imaging sensor (i.e., data representing the intensity of theimage at respective pixel positions). The processing element thenfilters the data to remove the noise associated with the signal at eachpixel position. More specifically, the processing element uses the datarepresenting the intensity of the image at respective pixel positions,as well as the analogue gain associated with the digital imaging sensor,to determine the standard deviation of the noise associated withrespective pixel positions. The adaptive filter can then use thestandard deviation to filter the noise from each pixel position. Thefiltered signal can then be output to an image reconstruction unit,which performs various reconstruction functions including, for example,sharpening the image and/or performing contrast adjustments. Accordingto exemplary embodiments, these subsequent stages may further benefitfrom the improved noise modeling provided by exemplary embodiments ofthe present invention.

In general, exemplary embodiments of the present invention provide animprovement over the known prior art since, unlike conventional noisemodels for de-noising, which use a unique constant σ for every pixel ofthe image, according to the noise model of exemplary embodiments, σ is aparameterized function, where the parameters are key characteristics ofthe sensor (p=pedestal level, q=quantum efficiency, and α=analoguegain). In other words, unlike conventional noise models, the generalsignal-dependent noise model of exemplary embodiments has beenreformatted in a form where the parameters of the signal-dependent noiseare related to the characteristics of the sensor.

Because the parameters p and q are fixed and depend only on the specificsensor installed in the device, they can be factory-defined and, in someinstances, might be reconfigured or recalibrated by the user or servicepersonnel. In addition, the analogue gain (α) parameter for the gain isknown, since the sensor automatic parameter selection can provide thechosen gain values to the rest of the imaging chain. Alternatively, thegain parameter can be extrapolated from noise-measurement on thenon-exposed portion of the sensor. In one exemplary embodiment, asmentioned above, the specific standard-deviations defined by the modelcorresponding to these sensor parameters can be placed in a LUTaccording to the pixelwise intensity, and fetched dynamically by theadaptive filtering procedure (e.g., calculating the exponents infloating point is slower than desired in some software platforms, suchas Symbian).

In addition to the foregoing, the noise model of exemplary embodimentsprovides an improvement over the known prior art because it isspecifically targeted at being implemented inside the imaging chain.This is in contrast to being used for hardware implementations where,for example, an analytical engineer desires to know characteristics,such as, the noise of the input current. In particular, as describedabove, the noise model of exemplary embodiments of the present inventionis applied at the first stage of the imaging chain to the digital datathat can be processed (i.e., the raw data immediately after the sensorhas obtained it).

FIGS. 5A and 5B provide an illustration of the superior quality of therestoration of the image that is obtained by modeling the noiseaccording to Equation 24. In particular, FIG. 5A presents the raw datafrom a cameraphone's CMOS sensor, R (i.e., red) channel, 1 ms exposure,while FIG. 5B provides the reconstructed image using LPA-ICI (LocalPolynomial Approximation-Intersection of Confidence Intervals) adaptivemethod, which uses the proposed noise model.

Mobile Station:

Reference is now made to FIG. 6, which illustrates one type ofelectronic device that would benefit from embodiments of the presentinvention. As shown, the electronic device may be a mobile station 10,and, in particular, a cellular telephone or cameraphone. It should beunderstood, however, that the mobile station illustrated and hereinafterdescribed is merely illustrative of one type of electronic device thatwould benefit from the present invention and, therefore, should not betaken to limit the scope of the present invention. While severalembodiments of the mobile station 10 are illustrated and will behereinafter described for purposes of example, other types of mobilestations, such as digital cameras, webcams, personal digital assistants(PDAs), pagers, laptop computers, as well as other types of electronicsystems including both mobile, wireless devices and fixed, wirelinedevices, can readily employ embodiments of the present invention.

The mobile station includes various means for performing one or morefunctions in accordance with exemplary embodiments of the presentinvention, including those more particularly shown and described herein.It should be understood, however, that one or more of the entities mayinclude alternative means for performing one or more like functions,without departing from the spirit and scope of the present invention.More particularly, for example, as shown in FIG. 6, in addition to anantenna 302, the mobile station 10 includes a transmitter 304, areceiver 306, and means, such as a processing device 308, e.g., aprocessor, controller or the like, that provides signals to and receivessignals from the transmitter 304 and receiver 306, respectively. Thesesignals include signaling information in accordance with the airinterface standard of the applicable cellular system and also userspeech and/or user generated data. In this regard, the mobile stationcan be capable of operating with one or more air interface standards,communication protocols, modulation types, and access types. Moreparticularly, the mobile station can be capable of operating inaccordance with any of a number of second-generation (2G), 2.5G and/orthird-generation (3G) communication protocols or the like. Further, forexample, the mobile station can be capable of operating in accordancewith any of a number of different wireless networking techniques,including Bluetooth, IEEE 802.11 WLAN (or Wi-Fi®), IEEE 802.16 WiMAX,ultra wideband (UWB), and the like.

It is understood that the processing device 308, such as a processor,controller or other computing device, includes the circuitry requiredfor implementing the video, audio, and logic functions of the mobilestation and is capable of executing application programs forimplementing the functionality discussed herein. For example, theprocessing device may be comprised of various means including a digitalsignal processor device, a microprocessor device, and various analog todigital converters, digital to analog converters, and other supportcircuits. The control and signal processing functions of the mobiledevice are allocated between these devices according to their respectivecapabilities. The processing device 308 thus also includes thefunctionality to convolutionally encode and interleave message and dataprior to modulation and transmission. The processing device canadditionally include an internal voice coder (VC) 308A, and may includean internal data modem (DM) 308B. Further, the processing device 308 mayinclude the functionality to operate one or more software applications,which may be stored in memory. For example, the controller may becapable of operating a connectivity program, such as a conventional Webbrowser. The connectivity program may then allow the mobile station totransmit and receive Web content, such as according to HTTP and/or theWireless Application Protocol (WAP), for example.

The mobile station 10 may further comprise an image capturing device 328(e.g., a digital camera, as is known by those of ordinary skill in theart) for capturing digital images for processing in the manner describedherein. In particular, the image capturing device 328 of one exemplaryembodiment may include components, such as a lens (not shown), afocusing mechanism (also not shown), for automatically or manuallyfocusing the image viewable via the lens, and the like. The imagecapturing device 328 further includes a digital imaging sensor (e.g.,CMOS or CCD sensor) 326, which converts the image into a digital signal.As discussed above, the output of the digital imaging sensor 326 (i.e.,the raw data representing the intensity of the image at respective pixelpositions) is used to derive the signal-dependent noise model based onone or more parameters associated with characteristics of the digitalimaging sensor (e.g., analogue gain, pedestal level and quantumefficiency).

The mobile station may also comprise means such as a user interfaceincluding, for example, a conventional earphone or speaker 310, a ringer312, a microphone 314, a display 316, all of which are coupled to thecontroller 308. The user input interface, which allows the mobile deviceto receive data, can comprise any of a number of devices allowing themobile device to receive data, such as a keypad 318, a touch display(not shown), a microphone 314, or other input device. In embodimentsincluding a keypad, the keypad can include the conventional numeric(0-9) and related keys (#, *), and other keys used for operating themobile station and may include a full set of alphanumeric keys or set ofkeys that may be activated to provide a full set of alphanumeric keys.Although not shown, the mobile station may include a battery, such as avibrating battery pack, for powering the various circuits that arerequired to operate the mobile station, as well as optionally providingmechanical vibration as a detectable output.

The mobile station can also include means, such as memory including, forexample, a subscriber identity module (SIM) 320, a removable useridentity module (R-UIM) (not shown), or the like, which typically storesinformation elements related to a mobile subscriber. In addition to theSIM, the mobile device can include other memory. In this regard, themobile station can include volatile memory 322, as well as othernon-volatile memory 324, which can be embedded and/or may be removable.For example, the other non-volatile memory may be embedded or removablemultimedia memory cards (MMCs), Memory Sticks as manufactured by SonyCorporation, EEPROM, flash memory, hard disk, or the like. The memorycan store any of a number of pieces or amount of information and dataused by the mobile device to implement the functions of the mobilestation. For example, the memory can store an identifier, such as aninternational mobile equipment identification (IMEI) code, internationalmobile subscriber identification (IMSI) code, mobile device integratedservices digital network (MSISDN) code, or the like, capable of uniquelyidentifying the mobile device. The memory can also store content. Thememory may, for example, store computer program code for an applicationand other computer programs. For example, in one embodiment of thepresent invention, the memory may store computer program code fordetermining the standard deviation of the noise associated with thedigital image as a function of the intensity of the signal at respectivepixel positions.

The apparatus, method, mobile station and computer program product ofexemplary embodiments of the present invention are primarily describedin conjunction with mobile communications applications. It should beunderstood, however, that the apparatus, method, mobile station andcomputer program product of embodiments of the present invention can beutilized in conjunction with a variety of other applications, both inthe mobile communications industries and outside of the mobilecommunications industries. For example, the apparatus, method, mobilestation and computer program product of exemplary embodiments of thepresent invention can be utilized in conjunction with wireline and/orwireless network (e.g., Internet) applications.

CONCLUSION

As described above and as will be appreciated by one skilled in the art,embodiments of the present invention may be configured as an apparatus,method and mobile station. Accordingly, embodiments of the presentinvention may be comprised of various means including entirely ofhardware, entirely of software, or any combination of software andhardware. Furthermore, embodiments of the present invention may take theform of a computer program product on a computer-readable storage mediumhaving computer-readable program instructions (e.g., computer software)embodied in the storage medium. Any suitable computer-readable storagemedium may be utilized including hard disks, CD-ROMs, optical storagedevices, or magnetic storage devices.

Exemplary embodiments of the present invention have been described abovewith reference to block diagrams and flowchart illustrations of methods,apparatuses (i.e., systems) and computer program products. It will beunderstood that each block of the block diagrams and flowchartillustrations, and combinations of blocks in the block diagrams andflowchart illustrations, respectively, can be implemented by variousmeans including computer program instructions. These computer programinstructions may be loaded onto a general purpose computer, specialpurpose computer, or other programmable data processing apparatus toproduce a machine, such that the instructions which execute on thecomputer or other programmable data processing apparatus create a meansfor implementing the functions specified in the flowchart block orblocks.

These computer program instructions may also be stored in acomputer-readable memory that can direct a computer or otherprogrammable data processing apparatus to function in a particularmanner, such that the instructions stored in the computer-readablememory produce an article of manufacture including computer-readableinstructions for implementing the function specified in the flowchartblock or blocks. The computer program instructions may also be loadedonto a computer or other programmable data processing apparatus to causea series of operational steps to be performed on the computer or otherprogrammable apparatus to produce a computer-implemented process suchthat the instructions that execute on the computer or other programmableapparatus provide steps for implementing the functions specified in theflowchart block or blocks.

Accordingly, blocks of the block diagrams and flowchart illustrationssupport combinations of means for performing the specified functions,combinations of steps for performing the specified functions and programinstruction means for performing the specified functions. It will alsobe understood that each block of the block diagrams and flowchartillustrations, and combinations of blocks in the block diagrams andflowchart illustrations, can be implemented by special purposehardware-based computer systems that perform the specified functions orsteps, or combinations of special purpose hardware and computerinstructions.

Many modifications and other embodiments of the inventions set forthherein will come to mind to one skilled in the art to which theseexemplary embodiments of the invention pertain having the benefit of theteachings presented in the foregoing descriptions and the associateddrawings. Therefore, it is to be understood that the embodiments of theinvention are not to be limited to the specific embodiments disclosedand that modifications and other embodiments are intended to be includedwithin the scope of the appended claims. Although specific terms areemployed herein, they are used in a generic and descriptive sense onlyand not for purposes of limitation.

1. An apparatus comprising: an input for receiving data representativeof an intensity of an image at a pixel position; a processor forfiltering the data to remove noise, wherein the processor filters thedata based on at least one parameter associated with one or morecharacteristics of a sensor through which the image was captured,wherein the processor determines a standard deviation of the noise basedon at least one of a quantum efficiency (q), a pedestal level (p), or ananalogue gain (α) associated with the sensor; and an output forproviding the filtered data.
 2. The apparatus of claim 1, wherein theprocessor filters the data based on a signal-dependent noise modeldefined based on the at least one parameter associated with one or morecharacteristics of the sensor.
 3. The apparatus of claim 1, wherein theprocessor determines the standard deviation of the noise as a functionof the intensity of the image at the pixel position.
 4. The apparatus ofclaim 3, wherein the processor determines the standard deviation of thenoise in accordance with σ^([α])(y)=q√{square root over (α(y−p))},wherein y represents the intensity of the image at the pixel position.5. The apparatus of claim 3, wherein the standard deviation of the noiseis independent of a color-channel and an exposure time associated withthe data.
 6. The apparatus of claim 1, wherein the input receives thedata directly from the sensor.
 7. The apparatus of claim 1, wherein theoutput provides the filtered data to an image reconstruction unit. 8.The apparatus of claim 1, wherein the processor calibrates the sensorusing a generic fixed target image.
 9. The apparatus of claim 8, whereinthe processor calibrates the sensor by: capturing a plurality of imagesof the generic fixed target image; averaging the intensities associatedwith the plurality of images captured; segmenting the average intensityinto a plurality of non-overlapping intensity regions, wherein theregions are defined irrespective of a shape or structure associated withthe generic fixed target image; computing a standard deviation forrespective images as a function of the intensities associated with theimage; averaging the standard deviations computed; determining at leastone parameter associated with one or more characteristics of the sensorbased at least in part on the average standard deviation; and generatinga sensor-specific signal-dependent noise model based at least in part onthe at least one parameter.
 10. A method comprising: receiving datarepresentative of an intensity of an image at a pixel position;filtering the data to remove noise using a processor, wherein filteringthe data comprises filtering the data based on at least one parameterassociated with one or more characteristics of a sensor through whichthe image was captured; determining a standard deviation of the noisebased on at least one of a quantum efficiency (q), a pedestal level (p),or an analogue gain (α) associated with the sensor; and providing thefiltered data.
 11. The method of claim 10, wherein filtering the datacomprises filtering the data based on a signal-dependent noise modeldefined based on the at least one parameter associated with one or morecharacteristics of the sensor.
 12. The method of claim 10 furthercomprising: determining the standard deviation of the noise as afunction of the intensity of the image at the pixel position.
 13. Themethod of claim 12, wherein determining the standard deviation of thenoise comprises determining the standard deviation of the noise inaccordance with σ^([α])(y)=q√{square root over (α(y−p))}, wherein yrepresents the intensity of the image at the pixel position.
 14. Themethod of claim 12, wherein the standard deviation of the noise isindependent of a color-channel and an exposure time associated with thedata.
 15. The method of claim 10, wherein receiving data representativeof an intensity of an image at a pixel position comprises receiving thedata directly from the sensor.
 16. The method of claim 10, whereinproviding the filtered data comprises providing the filtered data to animage reconstruction unit.
 17. The method of claim 10 furthercomprising: calibrating the sensor using a generic fixed target image.18. The method of claim 17, wherein calibrating the sensor furthercomprises: capturing a plurality of images of the generic fixed targetimage; averaging the intensities associated with the plurality of imagescaptured; segmenting the average intensity into a plurality ofnon-overlapping intensity regions, wherein the regions are definedirrespective of a shape or structure associated with the generic fixedtarget image; computing a standard deviation for respective images as afunction of the intensities associated with the image; averaging thestandard deviations computed; determining at least one parameterassociated with one or more characteristics of the sensor based at leastin part on the average standard deviation; and generating asensor-specific signal-dependent noise model based at least in part onthe at least one parameter.
 19. An apparatus comprising: at least oneprocessor; and at least one memory including computer program code, theat least one memory and the computer program code configured to, withthe at least one processor, cause an apparatus to perform at least thefollowing: receive data representative of an intensity of an image at apixel position; filter the data to remove noise, wherein the at leastone memory and the computer program code are further configured to, withthe at least one processor, cause an apparatus, to filter the data basedon at least one parameter associated with one or more characteristics ofa sensor through which the image was captured; determine a standarddeviation of the noise based on at least one of a quantum efficiency(g), a pedestal level (v), or an analogue gain (α) associated with thesensor; and provide the filtered data.
 20. The apparatus of claim 19,wherein, in order to filter the data to remove noise, the at least onememory and the computer program code are further configured to with theat least one processor, cause an apparatus to filter the data based on asignal-dependent noise model defined based on the at least one parameterassociated with one or more characteristics of the sensor.
 21. Theapparatus of claim 19, wherein the at least one memory and the computerprogram code are further configured to with the at least one processor,cause an apparatus to: determine the standard deviation of the noise asa function of the intensity of the image at the pixel position.
 22. Theapparatus of claim 21, wherein, in order to determine the standarddeviation of the noise, the at least one memory and the computer programcode are further configured to with the at least one processor, cause anapparatus to determine the standard deviation of the noise in accordancewith σ^([α])(y)=q√{square root over (α(y−p))}, wherein y represents theintensity of the image at the pixel position.
 23. The apparatus of claim21, wherein the standard deviation of the noise is independent of acolor-channel and an exposure time associated with the data.
 24. Theapparatus of claim 19 further comprising: a digital imaging sensorconfigured to provide the data representative of an intensity of animage at a pixel position.
 25. The apparatus of claim 19 furthercomprising: an image reconstruction unit configured to receive thefiltered data and to perform one or more reconstruction functions on thefiltered data.
 26. The apparatus of claim 19, wherein the at least onememory and the computer program code are fun her configured to with theat least one processor, cause an apparatus to: calibrate the sensorusing a generic fixed target image.
 27. The apparatus of claim 26,wherein, in order to calibrate the sensor, the at least one memory andthe computer program code are further configured to with the at leastone processor, cause an apparatus to: capture a plurality of images ofthe generic fixed target image; average the intensities associated withthe plurality of images captured; segment the average intensity into aplurality of non-overlapping intensity regions, wherein the regions aredefined irrespective of a shape or structure associated with the genericfixed target image; compute a standard deviation for respective imagesas a function of the intensities associated with the image; average thestandard deviations computed; determine at least one parameterassociated with one or more characteristics of the sensor based at leastin part on the average standard deviation; and generate asensor-specific signal-dependent noise model based at least in part onthe at least one parameter.
 28. An apparatus comprising: means forreceiving data representative of an intensity of an image at a pixelposition; means for filtering the data to remove noise, whereinfiltering the data comprises filtering the data based on at least oneparameter associated with one or more characteristics of a sensorthrough which the image was captured; means for determining a standarddeviation of the noise based on at least one of a quantum efficiency(q), a pedestal level (p), or an analogue gain (α) associated with thesensor; and means for providing the filtered data.
 29. The apparatus ofclaim 28, wherein the means for filtering the data to remove noisefurther comprises means for filtering the data based on asignal-dependent noise model defined based on the at least one parameterassociated with one or more characteristics of the sensor.
 30. Theapparatus of claim 28 further comprising: means for determining thestandard deviation of the noise as a function of the intensity of theimage at the pixel position.
 31. The apparatus of claim 30 wherein themeans for determining the standard deviation of the noise based on atleast one of a quantum efficiency (q), a pedestal level (p), or ananalogue gain (α) associated with the sensor further comprises means fordetermining the standard deviation of the noise in accordance withσ^([α])(y)=√{square root over (α(y−p))}, wherein y represents theintensity of the image at the pixel position.
 32. The apparatus of claim30, wherein the standard deviation of the noise is independent of acolor-channel and an exposure time associated with the data.
 33. Theapparatus of claim 28, wherein the means for receiving the datarepresentative of an intensity of an image at a pixel position comprisesmeans for receiving the data directly from the sensor.
 34. The apparatusof claim 28, wherein the means for providing the filtered data comprisesmeans for providing the filtered data to an image reconstruction unit.35. The apparatus of claim 28 further comprising: means for calibratingthe sensor using a generic fixed target image.
 36. The apparatus ofclaim 35, wherein the means for calibrating the sensor furthercomprises: means for capturing a plurality of images of the genericfixed target image; means for averaging the intensities associated withthe plurality of images captured; means for segmenting the averageintensity into a plurality of non-overlapping intensity regions, whereinthe regions are defined irrespective of a shape or structure associatedwith the generic fixed target image; means for computing a standarddeviation for respective images as a function of the intensitiesassociated with the image; means for averaging the standard deviationscomputed; means for determining at least one parameter associated withone or more characteristics of the sensor based at least in part on theaverage standard deviation; and means for generating a sensor-specificsignal-dependent noise model based at least in part on the at least oneparameter.
 37. A computer program product comprising at least onecomputer-readable storage medium having computer-readable program codeportions stored therein, the computer-readable program code portionscomprising: a first executable portion for receiving data representativeof an intensity of an image at a pixel position; a second executableportion for filtering the data to remove noise, wherein the secondexecutable portion is configured to filter the data based on at leastone parameter associated with one or more characteristics of a sensorthrough which the image was captured; a third executable portion fordetermining a standard deviation of the noise based on at least one of aquantum efficiency (q), a pedestal level (p), or an analogue gain (α)associated with the sensor; and a fourth executable portion forproviding the filtered data.
 38. The computer program product of claim37, wherein the second executable portion is configured to filter thedata based on a signal-dependent noise model defined based on the atleast one parameter associated with one or more characteristics of thesensor.
 39. The computer program product of claim 37, wherein thecomputer-readable program code portions further comprise: a fifthexecutable portion for determining the standard deviation of the noiseas a function of the intensity of the image at the pixel position. 40.The computer program product of claim 39, wherein the fifth executableportion is further configured to determine the standard deviation of thenoise in accordance with σ^([α])(y) q√{square root over (α(y−p))},wherein y represents the intensity of the image at the pixel position.41. The computer program product of claim 39, wherein the standarddeviation of the noise is independent of a color-channel and an exposuretime associated with the data.
 42. The computer program product of claim34, wherein the first executable portion is configured to receive thedata representative of an intensity of an image at a pixel positiondirectly from the sensor.
 43. The computer program product of claim 34,wherein the fourth executable portion is configured to provide thefiltered data to an image reconstruction unit.
 44. The computer programproduct of claim 34, wherein the computer-readable portions furthercomprise: a fifth executable portion for calibrating the sensor using ageneric fixed target image.
 45. The computer program product of claim44, wherein the fifth executable portion further comprises: a sixthexecutable portion for capturing a plurality of images of the genericfixed target image; a seventh executable portion for averaging theintensities associated with the plurality of images captured; an eighthexecutable portion for segmenting the average intensity into a pluralityof non-overlapping intensity regions, wherein the regions are definedirrespective of a shape or structure associated with the generic fixedtarget image; a ninth executable portion for computing a standarddeviation for respective images as a function of the intensitiesassociated with the image; a tenth executable portion for averaging thestandard deviations computed; an eleventh executable portion fordetermining at least one parameter associated with one or morecharacteristics of the sensor based at least in part on the averagestandard deviation; and a twelfth executable portion for generating asensor-specific signal-dependent noise model based at least in part onthe at least one parameter.